1. Yes, the one 30A hot is connected to both of the 50A socket hots. You naturally only have 30A available before the 30A breaker trips, spread between the two phases. (This does mean that any 240V circuits would not work, but essentially no RVs have 240V devices in them.)
2. Oftentimes people wire the EMS such that it comes between the shore power and the transfer switch, and so doesn't "see" the generator. However, it would not give this error when used with the generator because the built-in generator does bond neutral to ground at the generator. As the transfer switch is a three-pole switch, for the neutral and the two hots, this does not introduce a neutral/ground fault when connected to shore power.
If the built-in generator does not have neutral and ground bonded together, it's a faulty installation.
